MyMainScript

Sarthak Consul (16D100012),

Parthasarathi Khirwadkar (16D070001),

Bhishma Dedhia(16D170005)

tic;

Your code here

%reading in images

barbara = imread('../data/barbara.png');

TEM = imread('../data/TEM.png');

canyon = imread('../data/canyon.png');

retina = imread('../data/retina.png');

church = imread('../data/church.png');

Q2(a) Image Enhancement by Linear Contrast Stretching

where

is the pixel intensity after linear contrast stretching,

and

are the minimum and maximum values of pixel intensity in the input image. For coloured images, this is applied to each channel independently

%Pseudo code:

% a = input.min() //minimum pixel intensity of the input image

% b=input.max() //maximum pixel intensity of the input image

% T = Linear mapping from [a,b] to [0,255]

% (Hence T is a straight line from (a,0) to (b,255))

% for pixel in input:

% Output_intensity = T(pixel(intensity))

% end for;

%basic linear contrast stretching

tic;

barbara_linstretch = myLinearContrastStretching(barbara,'g');

my_imshow(barbara, 'Original Barbara');

my_imshow(barbara_linstretch, 'Linear Contrast Stretched Barbara');

toc;

Elapsed time is 1.868548 seconds.

tic;

TEM_linstretch = myLinearContrastStretching(TEM,'g');

my_imshow(TEM, 'Original TEM');

my_imshow(TEM_linstretch, 'Linear Contrast Stretched TEM');

toc;

Elapsed time is 2.986857 seconds.

tic;

canyon_linstretch = myLinearContrastStretching(canyon,'rgb');

my_imshow(canyon, 'Original Canyon');

my_imshow(canyon_linstretch, 'Linear Contrast Stretched Canyon');

toc;

Elapsed time is 4.657635 seconds.

tic;

church_linstretch = myLinearContrastStretching(church,'rgb');

my_imshow(church, 'Original Church');

Warning: Image is too big to fit on screen; displaying at 33%

my_imshow(church_linstretch, 'Linear Contrast Stretched Church');

Warning: Image is too big to fit on screen; displaying at 33%

toc;

Elapsed time is 34.955111 seconds.

toc;

Elapsed time is 35.015659 seconds.

Linear contrast stretching is ineffective in improving contrast in the church.png image. Linear contrast stretching aims to stretch the range of the image to span the entire possible range i.e 0-255. However, the input image contains pixel intensities of both 0 and 255 (or 1 in case of double) in all 3 channels. Thus the transormation is an identity transform, with the output identical to the input image.

Q2(b) Image Enhancement using Independent channel Histogram Equalisation

%Histogram Equalisation

tic;

barbara_he = myHE(barbara,'g');

my_imshow(barbara, "Original Barbara");

my_imshow(barbara_he, 'Histogram Equalised Barbara');

toc;

Elapsed time is 3.909700 seconds.

tic;

TEM_he = myHE(TEM,'g');

my_imshow(TEM, 'Original TEM');

my_imshow(TEM_he, 'Histogram Equalised TEM');

toc;

Elapsed time is 2.233294 seconds.

tic;

canyon_ind_he = myHE(canyon,'ind');

canyon_avg_he = myHE(canyon,'avg');

my_imshow(canyon, 'Original Canyon');

my_imshow(canyon_ind_he/255, 'Independent channel Histogram Equalised Canyon');

my_imshow(canyon_avg_he/255, 'Average Channel Histogram Equalised Canyon');

toc;

Elapsed time is 9.895772 seconds.

tic;

church_ind_he = myHE(church,'ind');

chruch_avg_he = myHE(church,'avg');

my_imshow(church, 'Original Church');

Warning: Image is too big to fit on screen; displaying at 33%

my_imshow(church_ind_he/255, 'Independent channel Histogram Equalised Church');

Warning: Image is too big to fit on screen; displaying at 33%

my_imshow(chruch_avg_he/255, 'Average Channel Histogram Equalised Church');

Warning: Image is too big to fit on screen; displaying at 33%

toc;

Elapsed time is 111.121520 seconds.

tic;

my_imshow(retina, 'Original Retina');

Warning: Image is too big to fit on screen; displaying at 33%

retina_mask = imread('../data/retinaMask.png');

retina_ind_he = myHE(retina,'ind',retina_mask);

my_imshow(retina_ind_he/255, 'Independent channel Histogram Equalised Retina');

Warning: Image is too big to fit on screen; displaying at 33%

retina_avg_he = myHE(retina,'avg',retina_mask);

my_imshow(retina_avg_he/255, 'Averaged Channel Histogram Equalised Retina');

Warning: Image is too big to fit on screen; displaying at 33%

toc;

Elapsed time is 65.817651 seconds.

toc;

Elapsed time is 65.859684 seconds.

Applying Historgram equaisation independently for each channel results in a significant change in colour (as made abundantly clear for the retina image).

A variation of the independent channel histogram equalisation is the average channel histogram equalisation, where the average transform across channels is applied to all channels. While the colour scheme is retained in this enhancement, for certain applications (such as a pre-processing step before segmenting the eye blood vessels), independent channel histogram equalisation maybe preferred.

Comparing the performance of Histogram Equalisation and contrast stretching for image(5), it is clear that historgram equalisation is much better in improving contrast than linear contrast stretching. Linear contrast stretching's effects is greatly diminished if the range of pixel values is large, regardless of the number of such locations of extremely small or latge values. Histogram equalisation, on the other hand, has sufficient non-linearity to not be weakened by such factors.

Q2(c) Histogram Matching

% Histogram Matching

tic;

retina_mask = imread('../data/retinaMask.png');

retina_ref = imread('../data/retinaRef.png');

retina_ref_mask = imread('../data/retinaRefMask.png');

my_imshow(retina, 'Original Retina');

Warning: Image is too big to fit on screen; displaying at 33%

my_imshow(retina_ref, 'Reference Retina');

Warning: Image is too big to fit on screen; displaying at 33%

[HM_int,HM_op] = myHM(retina,retina_mask, retina_ref,retina_ref_mask);

my_imshow(HM_int, 'Histogram Equalised Retina');

Warning: Image is too big to fit on screen; displaying at 33%

my_imshow(HM_op, 'Histogram Matched Retina');

Warning: Image is too big to fit on screen; displaying at 33%

toc;

Elapsed time is 59.489826 seconds.

Simply applying histogram equalisation on mulit-channeled images (like RGB images), changes the colouring of the image (eg the retina is white not orange). This is an issue If we desired to only improve contrast, while maintaining the colouring, Histogram equilisation on the other hand is able to ensure the output image has better contrast without disturbing the colouring.

Masking is critical to ensure the best enhancement, else the black background would result in a spike in the histogram and distort the transformation.

Q2(d) Adaptive Histogram Equalisation`

% % Adaptive Histogram Equalisation`

tic;

my_imshow(barbara, "Original Barbara");

tic;

barbara_ahe_151 = myAHE(barbara,151);

my_imshow(barbara_ahe_151, 'Adaptive Histogram Equalised Barbara - window size = 151');

toc;

Elapsed time is 20.303398 seconds.

tic;

barbara_ahe_3 = myAHE(barbara,3);

my_imshow(barbara_ahe_3, 'Adaptive Histogram Equalised Barbara - window size = 3');

toc;

Elapsed time is 19.500725 seconds.

tic;

barbara_ahe_501 = myAHE(barbara,501);

my_imshow(barbara_ahe_501, 'Adaptive Histogram Equalised Barbara - window size = 501');

toc;

Elapsed time is 22.399424 seconds.

my_imshow(TEM, 'Original TEM');

tic;

TEM_ahe_231 = myAHE(TEM,231);

my_imshow(TEM_ahe_231, 'Adaptive Histogram Equalised TEM - window size = 231');

toc;

Elapsed time is 33.301417 seconds.

tic;

TEM_ahe_3 = myAHE(TEM,3);

my_imshow(TEM_ahe_3, 'Adaptive Histogram Equalised TEM - window size = 3');

toc;

Elapsed time is 30.092696 seconds.

tic;

TEM_ahe_543 = myAHE(TEM,543);

my_imshow(TEM_ahe_543, 'Adaptive Histogram Equalised TEM - window size = 543');

toc;

Elapsed time is 36.910215 seconds.

% canyon_avg_ahe = myAHE(canyon,'avg');

my_imshow(canyon, 'Original Canyon');

tic;

canyon_ahe_421 = myAHE(canyon,421);

my_imshow((canyon_ahe_421)/255, 'Independent channel Adaptive Histogram Equalised Canyon- window size = 421');

toc;

Elapsed time is 70.083705 seconds.

tic;

canyon_ahe_23 = myAHE(canyon,23);

my_imshow((canyon_ahe_23)/255, 'Independent channel Adaptive Histogram Equalised Canyon- window size = 23');

toc;

Elapsed time is 59.113915 seconds.

tic;

canyon_ahe_721 = myAHE(canyon,721);

my_imshow((canyon_ahe_721)/255, 'Independent channel Adaptive Histogram Equalised Canyon- window size = 721');

toc;

Elapsed time is 113.224265 seconds.

toc;

Elapsed time is 113.286015 seconds.

The optimum window size for best contrast is dependent on the image. Clearly, the small window size amplifies noise a lot. In its extreme, the output resembles noise (eg. Applying AHE with window size=3 for canyon). For coloured images, smaller window sizes also distorts the colour scheme.

On the flip side if the window size is too large, the transformation is simlar to that of vanilla Histogram Equalisation and contrast improvement is lower. This is explained by the fact that to improve contrast, local pixel intensity is of importanct, if the window is too large, the histogram obtained is less sensitive to the pixel intensties in the immediate neighbourhood of the pixel.

Q2(e) Contrast-limited Adaptive Histogram Equalisation`

% Contrast-limited Adaptive Histogram Equalisation`

tic;

my_imshow(barbara, "Original Barbara");

barbara_thresh = 0.01;

tic;

barbara_clahe_full = myCLAHE(barbara,151,barbara_thresh);

my_imshow(barbara_clahe_full, cat(2,'CL-Adaptive Histogram Equalised Barbara, h=',num2str(barbara_thresh)));

toc;

Elapsed time is 32.733395 seconds.

tic;

barbara_clahe_half = myCLAHE(barbara,151,barbara_thresh/2);

my_imshow(barbara_clahe_half, cat(2,'CL-Adaptive Histogram Equalised Barbara, h=',num2str(barbara_thresh/2)));

toc;

Elapsed time is 22.447842 seconds.

my_imshow(TEM, 'Original TEM');

TEM_thresh = 0.008;

tic;

TEM_clahe_full = myCLAHE(TEM,51,TEM_thresh);

my_imshow(TEM_clahe_full, cat(2,'CL-Adaptive Histogram Equalised TEM, h=',num2str(TEM_thresh)));

toc;

Elapsed time is 35.406121 seconds.

tic;

TEM_clahe_half = myCLAHE(TEM,51,TEM_thresh/2);

my_imshow(TEM_clahe_half, cat(2,'CL-Adaptive Histogram Equalised TEM, h=',num2str(TEM_thresh/2)));

toc;

Elapsed time is 34.526884 seconds.

my_imshow(canyon, 'Original Canyon');

canyon_thresh = 0.01;

tic;

canyon_clahe_full = myCLAHE(canyon,301,canyon_thresh);

my_imshow((canyon_clahe_full)/255, cat(2,'Independent channel CL-Adaptive Histogram Equalised TEM, h=',num2str(canyon_thresh)));

toc;

Elapsed time is 70.570069 seconds.

tic;

canyon_clahe_half = myCLAHE(canyon,301,canyon_thresh/2);

my_imshow((canyon_clahe_half)/255, cat(2,'Independent channel CL-Adaptive Histogram Equalised TEM, h=',num2str(canyon_thresh/2)));

toc;

Elapsed time is 70.334731 seconds.

toc;

Elapsed time is 70.881671 seconds.

The histogram-threshold parameter governs the behavior of the CLAHE transform. If h is very small, the output would be very similar to the input while if h is large, the output would match that of AHE, for the same window size.

For better contrast, we desire to use smaller window sizes for AHE, however this also applifies noise. CLAHE enables us to use smaller windows, with lesser noise in the output.

This is best highlighted by the fact that for TEM, we had to resort to using a larger window size of 231 for AHE, but CLAHE can give similar enhancement with a window size of just 51.

toc;

Elapsed time is 70.915576 seconds.